Article exhibiting reduced frictional drag in fluids



Aug. 28, 1962 F. w. BOGGS 3,051,599

ARTICLE EXHIBITING REDUCED FRICTIONAL DRAG IN FLUIDS Filed June 25, 1958 RAT/6' 0/ 0/?46 COE'FF/C/E/VT 0F COVERED MODEL? 70 7/7647 OF THE (HG/0 JWfiF/ICE MODEL l M0004? 0F EZAJ'T/C/T) Eg Z INVENTOR.

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ATTORNEY United States Patent 3,051,599 ARTICLE EXHIBITING'REDUCED FRICTIONAL DRAG IN FLUIDS Fitzhugh W. Boggs, Upper Montclair, N.J., assignor to United States Rubber Company, New York, N.Y., a corporation of New Jersey Filed June 23, 1958, Ser. No. 743,673

4 Claims. (Cl. 15443) This invention relates to improvements in the method of reducing the frictional drag on an object moving in a fluid medium wherein turbulence in the boundary layer between the object and the medium is reduced by applying to the surface of the object a thin, flexible, resilient covering or coating having certain characteristics.

In my co-pending application, Serial No. 712,216, filed January 30, 1958, I have shown that the frictional drag may be reduced materially when the resilient covering applied has an energy absorption per bounce of between 0.5 and 0.9 and a modulus of elasticity in the range from 25 to 350 psi, the thickness of the covering being at least A inch.

It is an object of the present invention to make modifications in the surface covering disclosed in the abovementioned co-pending application to permit greater reductions in drag than were heretofore possible. It is a further object of the present invention to provide an improved surface covering which will maximize boundary layer stability at every point along the entire length of the object as it moves through the fluid medium.

Other objects and advantages of this invention will appear during the following detailed description of a preferred form of the invention, reference being had to the accompanying drawings forming a part of this specification, in which:

FIGURE 1 shows a model incorporating the features of this invention;

FIGURE 2 is a graph showing the relationship of the ratio of the drag coefficient of a cylinder covered according to the present invention to an uncovered cylinder, to the reciprocal of the modulus of elasticity for various Reynolds numbers.

In accordance with these objectives, I propose to reduce the frictional drag on an object moving in a fluid medium by applying to the objects surface a thin covering having properties within the limits specified in the above-mentioned co-pending application yet which vary progressively along the entire length of the object. The properties concerned include the damping character, or hysteresis, the modulus and the thickness of the surface mum boundary layer stability at only one value of the Reynolds number, and thus to achieve maximum drag reduction for the object as a whole it is necessary to change the characteristics of the covering as the Reynolds number changes, Only by having the characteristics of the surface covering provide maximum boundary layer stability at each differing value of Reynolds number along the objects length can minimum frictional drag be obtained.

Three quantities which influence the damping out of turbulence by a covering on the surface of an object are the thickness of the covering, its modulus and its hysteresis. The thickness of the covering is self-explanatory. The modulus of any material is the ratio of the stress sustained by the material to the strain experienced. In the context of this specification it is defined as follows: the initial slope of the stress-strain curve is extrapolated from the origin to the abscissa representing 100% elongation. The value of the stress corresponding to this point is the modulus referred to throughout this specification. The hysteresis of a covering is a measure of the energy absorption of the material. There are a number of ways of measuring the hysteresis. Since I am interested in hysteresis at high frequency, I have used rebound as a measure: the higher the rebound, the lower the hysteresis. I have used the approximate relation:

1.00-percent rebound Modulus Although this relation is neither exact nor dimensionally correct, it is a measure of the hysteresis as it is used in this specification.

As has been stated above, these three quantities must vary as the Reynolds number varies along the length of the object. I have found that to obtain maximum boundary layer stability at any point on the surface it is necessary to prescribe any two of the quantities after the third has been arbitrarily predetermined. Thus, if I wish to reduce the drag of a given object moving through water at a certain operating speed and, further, to select a surface covering that will maximize boundary layer stability at every point along the objects length, I can proceed in any of three different ways. I can hold the thickness of the covering constant over the entire length of the object and vary the modulus and hysteresis. Or, I

Hysteresis:

I can hold the modulus constant and vary the thickness covering and I have discovered certain definite rules by which to specify this variation.

' Whether the flow of a fluid past a smooth surface is laminar or turbulent is determined by two quantities, the velocity of the maximum flow and the Reynolds number. 'By the velocity of the maximum flow we mean, in the case of an object moving through water, the actual velocity of the object with respect to the water. Practically, this is a velocity of the object itself. The Reynolds number is a non-dimensional quantity proportional to the velocity and to the length along the object from the bow and inversely proportional to the kinematic viscosity of the medium. It may be expressed by the following relationship:

VelocityXlength from bow 1 Reynold S Kinematic viscosity and hysteresis. Or, finally, I can hold the hysteresis of the covering constant and vary the modulus and the thickness.

Assuming an object moving in water, if I choose to hold the thickness of the surface covering constant over the entire length of the object, I must vary the modulus and hysteresis so that the modulus will be proportional to the reciprocal of the Reynolds number and the hysteresis will be proportional to the reciprocal of the square root 7 of the Reynolds number. Assuming constant velocity and constant kinematic viscosity, and knowing that the Reynolds number increases linearly from bow to stern, I must vary the modulus proportionally to the reciprocal of the Reynolds number, and the hysteresis must vary proportionally to the reciprocal of the square root of the Reynolds number, as the latter varies from bow to stern. This is shown by the following two relations:

' (Reynolds number) To apply these relations to a specific example, a model was made as shown in FIG. 1. The overall length, L,

The radius of curvature at 3 :10.8 was chosen equal to 0.100 inch.

Assuming it is desired to apply a 75 inch thick surface covering to the cylindrical portion of this model, it will be necessary to evaluate actual constants for the above-mentioned general relations. To do this we proceed as follows. The drag on the model is measured both in the case of a rigid surface and when coated with rubber of differing moduli but having the same hysteresis and thickness. The measurement is made for a variety of Reynolds numbers which are obtained by varying the speed, the distances from the tip to the rubber covering being known as above specified. If now I plot the ratio of the drag coefiicient of the covered cylinder to the uncovered cylinder as a function of the reciprocal of the modulus for each Reynolds number measured, I obtain a family of curves, each of which has a minimum, as shown in FIG. 2. The minima occur at different points for different Reynolds numbers and the values at the minima differ for each. Among these Reynolds numbers there is one which gives the lowest minimum, namely, 3x10 which corresponded to a speed of 10 miles per hour. The modulus corresponding to this minimum, 38 p.s.i., is the best modulus for the hysteresis and thickness at this particular Reynolds number. If I substitute these values into the above-mentioned general relations, I obtain the following two equations:

(Reynolds number) where the velocity is expressed in miles per hour and the modulus in p.s.i.

Assuming that maximum drag reduction is desired for this 'model at a velocity of 10 miles per hour, the fig inch thick surface covering must have a modulus equal to 38 p.s.i. for a Reynolds number of 3 X10 At a point twice as far from the bow, where the Reynolds number will be twice as large, this value of the modulus must be halved, etc. Similarly, where a value of the hysteresis equal to .286 will be required for a Reynolds number of 3x10, doubling the length from the how will require the hysteresis to be divided by the square root of 2. Thus it will be possible to specify these two quantities, modulus and hysteresis, at every point along the models length.

Where instead I choose to hold the modulus of the surface covering constant along the entire length of the object, I must vary the thickness and hysteresis of the surface covering so that both increase progressively from how to stem proportionally to the square root of the (ii. Reynolds number, as will be seen from the following two relations:

(Reynolds number) (Reynolds number) (Velocity) Assuming, again for the model of FIG. 1, a surface covering having a uniform modulus of 38 p.s.i. substitution of the values of thickness, hysteresis and velocity for the Reynolds number showing the lowest minimum from the above-mentioned family of curves permit these relations to be reduced to the following two equations:

(Reynolds number) 1/2 Velocity Hysteresis:

Thickness 1 .08X 10 (Reynolds number) (Velocity) Assuming, as previously, a design velocity of 10 miles per hour, at a point along the length of the model Where the Reynolds number equals 3X10 the thickness of the surface covering must be approximately 7 inch. At a point twice as far from the bow, where the Reynolds number has increased by a factor of 2, the thickness will be approximately .45 inch. Thus it will be possible to specify optimum values of thickness and hysteresis for this constant-modulus surface covering at every point along the models length.

Finally, if I choose to hold the hysteresis of the surface covering constant along the length of the object, I must decrease the modulus and increase the thickness from fore to aft. In this case the modulus must vary proportionally to the reciprocal of the square root of the Reynolds number and the thickness must increase pro portion-ally to the fourth root of the Reynolds number. This is shown by the following two relations:

N (Velocity) 2 Modulus (Reynolds number) 1/2 Hysteresis 1 .65 X 10 Thickness:

Modulus 670 7 1/4 T k 447 W Veloc1ty Again assuming a design velocity of 10 miles per hour for the model of FIG. 1 and a surface covering having a hysteresis value equal to .28 6, at a point along the length of the model where the Reynolds number equals 3 x10 the modulus must be 38 p.s.i. and the thickness must be 71 inch. At a point along the length of the model twice as far from the bow, where the Reynolds number has increased by a factor of 2, the modulus must be decreased to approximately 27 p.s.i. and the thickness must be increased to approximately .23 inch. Thus it is possible to specify, for a surface covering having a hysteresis equal to .286, the optimum values of both modulus and thickness for every point along the models length.

As was mentioned in my co-pending application, Serial No. 712,216, an elastomeric compound, such as rubber, is a suitable substance out of which to make the surface covering. Varying the properties of this rubber covering along the length of the object to be covered can be efiected in a number of ways. The modulus of the rubber covering may be progressively decreased by use of a series of cover strips of successively lower degrees of cure, lower sulfur, or less accelerator, or of succes- 75 sively lower content of reinforcing filler or higher content 5. of softener or plasticizer, or in any other way which is well known to the rubber compounder. The modulus may also be varied by using a series of rubber strips of varying porosity produced by known methods of producing sponge rubber, such spongy strips preferably having a smooth unbroken skin of rubber on the surface. Likewise, the hysteresis of the rubber covering may be varied by known methods, such as varying the type of rubber used, for example, by selecting Hevea or butyl, or by varying the amount of plasticizer or the amount of reinforcing filler, or by LH processing as shown in US. Patent No. 2,118,601. For example, the two formulations given below are to illustrate that it is possible to produce rubber compounds having comparable moduli but widely difienng hystereses:

Formulation 1 Formulation 2 Item Parts by Item Parts by Weight Weight Smoked Sheet 100 Butyl rubber 100 N on-volatile aromatic Channel black 20 hydrocarbon oil (rub- Phenyl-beta-naphthylber extender) 50 amine. 1 Zine oxide- Zinc oxide 5 Stearic acid 5 Stearic acid 1 2-Benzo thiazyl disul- 2-Mercaptobenzothia fide 2 zole 2 Tetramethylthiuram Tetramethylthiuram monosulfide 0. 5 disulfide 2 4 Sulfur 3 Modulus (Shore Du- Modulus (Shore D rorneter A) 46 rometer A) 46 Hysteresis (Rebound) 57% Hysteresis (Rebound)- 7% S1m1larly, the followm g two formulations have comparable hystereses but widely differing moduli:

Formulation 3 Formulation 4 Item Parts by Item Parts by Weight Weight Smoked Sheet 100 Smoked Sheet 100 Acetone-Diphenyl- Acetone-DiphenyL amine condensate 1 amine condensate 1 N,N- diphenyl-p-phen- N,N-diphenyl-p-phenylenediamine 0. 4 ylenediamine 0. 4 5 Zinc oxide- 5 Stearic acid 5 Stearic acid 5 2-Benzothiazyl disulfide 2 2-Benzothiazyl disul- Tetramethylthiuram fide 2 monosulfide 0. 5 Tetramethylthiuram Sulfur 2. 5 monosulfide 0. 5 Modulus (Shore Du- Sulfur 5 rometer A) 54 Modulus (Shore Du- Hysteresis (Rebound) 70% rometer A) 6O Hysteresis (Rebound) 69% Thus, I have shown that it is entirely possible to vary these two properties, modulus and hysteresis, of a rubber covering at will by varying the compositions of the formulations and the type of rubber used. In practice I divide the length of the object to be covered into a convenient number of sections, preferably selecting shorter sections near the bow where the percent change in Reynolds number is the greatest. A rubber formulation having suitable properties is selected for each such section so that the object when finally covered will have adequately graduated properties.

The thickness of the rubber covering may be varied in any number of difierent ways. For instance, the covering may be built up of successive zones of diflerent thicknesses of difierent rubbers, or by having increasing numbers of plies of different rubbers laminated together. There are many other methods of varying the thickness and the properties according to these rules which will be apparent to those skilled in the art. In all cases a final smooth surface may be obtained by molding or by grinding to a smooth contour after a wrapped cure.

Having thus described my invention, what I claim and desire to protect by Letters Patent is:

1. An object designed for movement through a fluid medium and exhibiting optimum drag-reducing characteristics at a design velocity V, having on its fluid-contacting surfaces a thin resilient elastomeric covering having any one of its properties of thickness, modulus and hysteresis constant; said covering being further characterized in that when its thickness is constant, its modulus varies along the length of said object from bow to stem substantially proportionally to and its hysteresis v-aries along the length of said object from bow to stem substantially proportionally to along the length of said object from bow to stem substantially proportionally to and its modulus varies along the length of said object from bow to stern substantially proportionally to Where in all cases V is said design velocity and R, is the Reynolds number at said design velocity expressed as VX distance from how Kinematic viscosity of fluid medium 2. An object designed for movement through a fluid medium and exhibiting optimum drag-reducing characteristics at a design velocity V, having on its fluid-contacting surfaces a thin resilient elastomeric covering of constant thickness, said covering having a modulus which varies along the length of said object from how to stern substantially in accordance with the equation 4 Modulus= and a hysteresis which varies along the length of said object from bow to stern substantially in accordance with the equation 2 Hysteresis g l where V is said design velocity, A and B are constants, and R is the Reynolds number at said design velocity expressed as R VX distance from bow Kinematic viscosity of fluid medium 3. An object designed for movement through a fluid medium and exhibiting optimum drag-reducing characteristics at a design velocity V, having on its fluid-contacting surfaces a thin resilient elastomeric covering of constant modulus, said covering having a thickness which varies Thickness:

D ilz 2 where V is said design velocity, C and D are constants,

and R is the Reynolds number at, said design velocity expressed as Hysteresis:

VXdistance from bow Kinematic viscosity of fluid medium 4. An object designed for movement through a fluid medium and exhibiting optimum drag-reducing characteristics at a design velocity V, having on its fluid-contacting surfaces a thin resilient elastomeric covering of constant hysteresis, said covering having a thickness which varies along the length of said object from bow to stem substantially in accordance with the equation and a modulus which varies along the length of said object Thickness:

from bow to stem substantially in-accordance with the equation FV RVIIZ where V is said design velocity, E and F are constants, and R is the Reynolds number at said design velocity expressed as R VXdistanee from bow Kinematic viscosity of fluid medium Modulus= References Cited in the file of this patent UNITED STATES PATENTS 1,315,356 Willard Sept. 9, 1919 1,426,907 Ramsey Aug. 22, 1922 2,332,196 Bjorksten Oct. 19, 1943 2,621,166 Schmidt et al Dec. 9, 1952 2,770,612 Schollenberger Nov. 13, 1956 FOREIGN PATENTS 373,666 Great Britain June 2, 1932 OTHER REFERENCES Industrial and Engineering Chemistry, vol. 48, No. 1, January 1956, pp. 59-63. 

1. AN OBJECT DESIGNED FOR MOVEMENT THROUGH A FLUID MEDIUM AND EXHIBITING OPTIMUM DRAG-REDUCING CHARACTERISTICS AT A DESIGN VELOCITY V, HAVING ON ITS FLUID-CONTACTING SURFACES A THIN RESILIENT ELASTOMERIC COVERING HAVING ANY ONE OF ITS PROPERTIES OF THICKNESS, MODULUS AND HYSTERESIS CONSTANT; SAID COVERING BEING FURTHER CHARACTERIZED IN THAT WHEN ITS THICKNESS IS CONSTANT, ITS MODULUS VARIES ALONG THE LENGTH OF SAID OBJECT FROM BOW TO STERN SUBSTANTIALLY PROPORTIONALLY TO 